I started indoor rock-climbing a few months ago, renting equipment from wherever I was climbing at. I've decided to take it a bit more seriously and invest in some equipment, and the first step are shoes. However, there's quite a lot to choose from and I'm not sure how to pick - the only difference I really notice is how they lace-up. What should I look for in a good shoe? To reiterate, I'm a beginner and I intend to climb just indoor (for the foreseeable future).
The only answer is comfortable shoes. It's quite possibly the only answer for a climber at any level, but certainly for beginners. You don't want shoes that will slip around, but most places will tell you to get them as tight as you can tolerate. That's way bogus. Get them comfortable. If as you progress they seem like they aren't tight enough, you'll get a tighter pair and still have the comfy pair for wearing on all of your warmups and easier climbs. The bottom line is that tight shoes are not good for you.
There are several types of shoe construction that impact how determining what the fit is going to be. For your first pair get a shoes that is synthetic; these shoes don't change size over time like leather shoes. Very important. They will fit as they fit at the store.
Also, avoid all performance oriented shoes. Such as downturned toes and radically asymmetric lasts. You might want a mildly asymetric last depending on the shape of your shoe. If your big toe is the longest, you want a mildly assymetric shoe. If one of your middle toes is the longest, you want the type of shoe that is symmetric, i.e. the long point at the end is centered, rather than the big toe part being the longest.
Outdoor Gear Lab wrote a pretty good article on the subject here: http://www.outdoorgearlab.com/Climbing-Shoe-Reviews/Buying-Advice
Quoting from this article:
If you are just starting out then you probably want a more comfortable, versatile, all-around shoe. Don't go for the aggressive down-turned shoes. Go for something that is not too tight and does not cost much. Shoes that close with Velcro are great because you can get them on and off fast. But a comfortable pair of lace-up shoes can be great as well.
Agressive downturn shapes are very helpful if you're climbing intermediate / advanced routes (5.10 / V4 and up). The shape of the shoe will bunch your toes together, and also will fit tighter. This will improve your ability to stand on smaller holds. Also, a downturn makes it easier to hook your toes on holds on overhanging routes.
But if you want to stick with a more comfortable shoe, that's OK to. Plenty of strong climbers will wear more comfortable shoes. If you find your toes slipping within the shoe as you try to stand on a hold, or you find the edge of the shoe flopping when you try to stand on a small hold, you'll know its time to switch to something more "agressive'.
Velcro will be more convenient to take on and off when you're switching between climbing and belaying (which you'll do a lot in the gym). But, most velcro shoes tend to be at least a little agressive.
Fit tends to be very personal, and most of the better shoes are made of leather, and actually stretch quite a bit, so even experienced climbers may have to buy more than one size if they switch brands. (The stretching tends to mold the shoe to your foot, so its really a desirable quality)
EDIT: I didn't address your question very well. Most beginner / comfort shoes are either 1) Inexpensive entry level shoes 2) traditional climbing shoes I think that nearly all "comfort" shoes (and traditional ones) are lace ups. You'll want a lace up shoe where all your toes lay flat. Also, you'll want to avoid an asymmetric, downturned shoe. Those two things (asymetric, downturned toe boxes that force your toes to curl up) are signs on an uncomfortable, more agressive shoe.
I do my rockclimbing in Vibram Fivefingers - they're not specifically designed for it but they work fine. Admittedly, my grip strength and arm strength is much more of a bottleneck for me at the moment than shoes.
Since you mentioned the only difference you saw is how they lace up, I'd suggest looking at shoes which have the lacing at an angle to the outside of your foot, rather than straight in line with your shin as shoes traditionally are. That keeps pressure off the top of your foot which can otherwise get very uncomfortable very quickly.